We were planning to make an HTML5 based chat app using the Websockets technology.
So my question is:
Which are the browsers that support <
As pointed out by NullPoiиteя and Orangepill, you could look at caniuse and html5please. So that was your first point/
Your second and third point are more for a fallback option. Well you could use polling. (see this answer for more info).
Well this is not in you question but a point you should consider (because you tagged it under php). Websockets have an active connection as long as the user is active. PHP is not ment for this, your server will flood into the connection and also a person with bad meaning could easily make sure the server is flooded.
This is because if you want it you need to set the time out limit on 0 (so never). So your server will stack up the requests until it is full. (how it acts as an connection dies I don't know).
If you wan't to use websockets and PHP you should look at pusher. I used this service for my own chat thingy. It works like magic and takes all the difficult things away from you.
I hope the info helps you develop a nive app